Force control in turning based on robust PI controller design

Real-time cutting force control is a very straightforward way to improve safety, performance and quality in rough turning operations. The main problem in controller design for force control is to achieve robustness. Several time-variable process parameters, such as the depth of cut, the spindle rotational speed and the specific cutting force, directly affect the closed-loop system gain and time constant. In this paper, two approaches to robust PI (proportional integral) controller design based on the internal model control (IMC) method are presented. The first approach treats the cutting process as a first-order system with a time-variable gain. By designing for highest process gain, the controller becomes robust, but perhaps a bit sluggish for the lower range of process gain. In the second approach, the cutting process is linearized by introducing non-linear transformations. In this way, the design may be based on a constant-gain system and the time-variable parameters may be considered as additive disturbances. This controller is somewhat faster than the first approach and shows almost identical behaviour over the entire operating range. Both controllers incorporate, in addition, simple parameter adaptation by gain scheduling with respect to spindle speed variations, in order to handle variations in the process time constant. The work presented in this paper shows that it is possible to achieve robust force control in turning using the common PI controller.